Solving fractional optimal control of systems described by the fractional order differential equations by using Bernoulli wavelets

Solving fractional optimal control of systems described by the fractional order differential equations by using Bernoulli wavelets

This paper presents a new numerical method for a class of fractional optimal control problems (FOCPs). The fractional derivative is described in the Caputo sense. The performance index of a FOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a set of fractional differential equations (FDEs). The method is based upon Bernoulli wavelets. The Bernoulli wavelets is first introduced. The operational matrices of fractional Riemann-Liouville integration and multiplication are derived and are utilized to reduce the given optimization problem to system of algebraic equations. Numerical solutions are presented to demonstrate the feasibility of the method.

This paper presents a new numerical method for a class of fractional optimal control problems (FOCPs). The fractional derivative is described in the Caputo sense. The performance index of a FOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a set of fractional differential equations (FDEs). The method is based upon Bernoulli wavelets. The Bernoulli wavelets is first introduced. The operational matrices of fractional Riemann-Liouville integration and multiplication are derived and are utilized to reduce the given optimization problem to system of algebraic equations. Numerical solutions are presented to demonstrate the feasibility of the method.